Our goal is to understand the quantitative principles whereby neural networks in the brain are formed during development. An ideal candidate to study these principles is the topographic projection from retina to optic tectum or mammalian superior colliculus. Axons of neighboring retinal cells terminate proximally in the superior colliculus thus forming a topographically precise representation of the visual world called topographic or retinotopic map. Coordinate axes are encoded in retina and in the target through graded expression of molecular labels, such as Eph receptor tyrosine kinases and their ligands, ephrins. Additional sharpening of projections is facilitated by correlated neural activity. In this proposal we will combine various developmental mechanisms in a single quantitative model and show how their interactions provide required precision of topographic mapping. The specific aims of this proposal include: i) How can one combine activity-dependent and activity-independent factors in the same model? ii) Why is the dynamics of axons and dendrites different during development? iii) What is the role of synaptic maturation in the axon and dendrite branch dynamics? Our project will help to understand the mechanisms whereby genetic program in the form of molecular labels and environmental information conveyed by correlated neural activity shape the developing neuronal connectivity. Our study will therefore provide insights on neurological conditions characterized by abnormal development of sensory function, including a possible effect of disruption of Eph/ ephrin pathways on impairment of visual processing in humans. Our model will aid in addressing developmental disabilities and neuro-degenerative diseases linked to defects in circuitry. All studies will be carried out in close collaboration with experimental groups. Expert advice will be solicited on all stages of the project.